Problem: A circle has a radius of $10$. An arc in this circle has a central angle of $324^\circ$. What is the length of the arc? {20\pi} {324^\circ} \color{#DF0030}{18\pi} {10}
Solution: First, calculate the circumference of the circle. $c = 2\pi r = 2\pi (10) = 20\pi$ The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{324^\circ}{360^\circ} = \dfrac{s}{20\pi}$ $\dfrac{9}{10} = \dfrac{s}{20\pi}$ $\dfrac{9}{10} \times 20\pi = s$ $18\pi = s$